Cryptology ePrint Archive: Report 2012/024

Variants of Waters' Dual-System Primitives Using Asymmetric Pairings

Somindu C. Ramanna and Sanjit Chatterjee and Palash Sarkar

Abstract: Waters, in 2009, introduced an important technique, called dual-system encryption,
to construct identity-based encryption (IBE) and related schemes. The resulting
IBE scheme was described in the setting of symmetric pairing. A key feature
of the construction is the presence of random tags in the ciphertext and
decryption key.
Later work by Lewko and Waters has removed the tags and proceeding through
composite-order pairings has led to a more efficient dual-system IBE scheme
using asymmetric pairings whose security is based on non-standard but static assumptions.
In this work, we have systematically simplified Waters 2009 IBE scheme in the
setting of asymmetric pairing. The simplifications retain tags used in the original
description. This leads to several variants, the first one of which
is based on standard assumptions and in comparison to Waters original scheme
reduces ciphertexts and keys by two elements each. Going through several stages
of simplifications, we finally obtain a simple scheme whose security can be
based on two standard assumptions and a natural and minimal extension of the
decision Diffie-Hellman problem for asymmetric pairing groups. The scheme itself is also
minimal in the sense that apart from the tags, both encryption and key generation
use exactly one randomiser each. This final scheme is more efficient than both the
previous dual-system IBE scheme in the asymmetric setting due to Lewko and Waters
and the more recent dual-system IBE scheme due to Lewko. We extend the IBE scheme to
hierarchical IBE (HIBE) and broadcast encryption (BE) schemes. Both primitives are
secure in their respective full models and have better efficiencies compared to
previously known schemes offering the same level and type of security.